These results cast severe doubts on the adequacy of SST models for RT data in choice reaction tasks and in memory scanning. It should be noted that the distributional inequality (equation (8)) is based on weaker assumptions and is thus a test of a broader class of SST models than the usually tested predictions concerning changes in mean RT which require the assumption of a constant mean duration per processing step. It seems therefore desirable to conduct the distributional tests under conditions where SST models have been shown to be successful with respect to mean RT's, in order to see whether the model passes the more general but possibly also more stringent test.
To my knowledge no data exist by which equation (11) (which relates the distributions from (n, r) and (n, r + 1) conditions to that of (n + 1, r + 1)) or equation (12) (which uses the distributions from (n, 1)-experiments to predict those from (n, r)-experiments,) can be tested. However, Bamber's data reported above are consistent with these predictions at least as far as the means are concerned. Bamber fitted an SST model to his data which uses the strong assumption of constant mean time per comparison, i.e.,
As Figure 2 shows, this model gives an excellent fit to the mean RT's on different-trials. It remains to be seen whether the model is also able to predict other distributional properties as well. One problem which is outside the scope of this paper is why the SST model's prediction totally breaks down on the same-trials where RT ought to be longest since the search has to be exhaustive but is actually shorter than on different-trials. This points to a shortcoming of the SST model for same-different experiments. Bamber [ 1969] proposed to fix it by assuming two separate parallel processes for the detection of sameness and of differences. This has some plausibility because of the excellent account of the mean RT's on different-trials which would be difficult to understand otherwise. At present, however, Bamber's suggestion is not widely accepted.
Bamber D., 1969. Reaction times and error rates for "same"-"different" judgments of multidimensional stimuli, Perception and Psychophysics 6, 169-174.
Donders F. C., 1969. Over de snelheid van psychische processen, translated in Attention and Performance. II ( W. G. Koster, ed.), Acta Psych. 30, 412-431.
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_____, 1973. Evidence against self-terminating memory search from properties of RT distributions, paper presented at the Annual Meeting of the Psychonomic Society, St. Louis, Mo.
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Publication information: Book title: Mathematical Psychology and Psychophysiology. Contributors: Stephen Grossberg - Editor. Publisher: American Mathematical Society. Place of publication: Providence, RI. Publication year: 1981. Page number: 317.
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